How come that we have well-orderd galaxies (from randomness) with the passage of time (many are in the process of evolution)?

How come elememts have combined together to form cells and eventually living beings.

How come humanbeings have started to live in an orderd state (cities, countries, etc.) from the disorderd/less ordered state of hunters?

When scientists say that the disorder is increasing, we are talking about the net entropy of the entire universe, which must increase according to the second law of thermodynamics. All of your examples represent *local* increases of order ... the second law tells us that the driving forces that allowed each of these cases to come about must have caused increases in entropy in the surrounding universe that were greater than the decrease in entropy represented in the local systems.

The first statement seems incorrect ... galaxies did not form out of randomness. They formed from clouds of interstellar atoms and molecules which represented a system with higher potential energy than a galaxy. The process of galaxy formation releases some of this energy back into the surrounding universe in such a way that the overall entropy is increased.

The second two statements reflect processes which required the input of significant amounts of energy, all of which ultimately derived from our sun. The nuclear processes that cause the sun to emit energy also increase its entropy, so that the net entropy changes of the universe from these processes are positive.

I realize that these answers may seem a bit solipsistic if you don't have a background in thermodynamics, so I will be happy to clarify as best I can if you have specific questions.

When scientists say that the disorder is increasing, we are talking about the net entropy of the entire universe, which must increase according to the second law of thermodynamics. All of your examples represent *local* increases of order ... the second law tells us that the driving forces that allowed each of these cases to come about must have caused increases in entropy in the surrounding universe that were greater than the decrease in entropy represented in the local systems.

The first statement seems incorrect ... galaxies did not form out of randomness. They formed from clouds of interstellar atoms and molecules which represented a system with higher potential energy than a galaxy. The process of galaxy formation releases some of this energy back into the surrounding universe in such a way that the overall entropy is increased.

The second two statements reflect processes which required the input of significant amounts of energy, all of which ultimately derived from our sun. The nuclear processes that cause the sun to emit energy also increase its entropy, so that the net entropy changes of the universe from these processes are positive.

I realize that these answers may seem a bit solipsistic if you don't have a background in thermodynamics, so I will be happy to clarify as best I can if you have specific questions.

1. Is there any proof of the second law of thermodnamics other than the mathematical one?

2. Suppose, the entropy of the universe becomes maximum. I think that would be the state of the bigbang or just after it. So, if entropy was already maximum, why it decreased to increase again.

How come that we have well-orderd galaxies (from randomness) with the passage of time (many are in the process of evolution)?

How come elememts have combined together to form cells and eventually living beings.

How come humanbeings have started to live in an orderd state (cities, countries, etc.) from the disorderd/less ordered state of hunters?

There is a probability derivation of the second law which shows that the increase in entropy is nothing else than saying for coin flips the most likely outcome is a ratio 1:1 between head and tails.
In order to use thermodynamics for galaxy or biology you need to indentify a correct notion of entropy which is basically based on [itex]S=\ln\Omega[/itex]. This won't be what you think is disorder.
The point is that high entropy is something completely different from what you think when it comes to more complex system rather than bouncing molecules. So thermodynamics doesn't apply the way you might think.
Look at the listhttp://www.math.utk.edu/~vasili/refs/darpa07.MathChallenges.html
There is a reason why there are so many problems which related to thermodynamics like problem, but can't be solved with it. It's just not useable there.

In my view SpectraCat has a too much specialized picture of thermodynamics, but I'm not in the mood to explain to him again. So I advice you to think about what [itex]S=\ln\Omega[/itex] means and how the second law derives from it. I've had a discussion with someone recently and I can post the results in a moment. Don't trust SpectraCat or even me. Make up your own thoughts!

How come elememts have combined together to form cells and eventually living beings.

How come humanbeings have started to live in an orderd state (cities, countries, etc.) from the disorderd/less ordered state of hunters?

Like SpectraCat said before, you have to look at it on a universe scale. Form wikipedia about entropy and life:

In short, according to Lehninger, "living organisms preserve their internal order by taking from their surroundings free energy, in the form of nutrients or sunlight, and returning to their surroundings an equal amount of energy as heat and entropy."

Yeah the entire universe is a closed system, whereas earth is not, so entropy in our planet can increase and decrease as well. Though, when I think about it, both the lowest state of entropy and the highest state of entropy of the universe have some similarities.

Yeah the entire universe is a closed system, whereas earth is not, so entropy in our planet can increase and decrease as well. Though, when I think about it, both the lowest state of entropy and the highest state of entropy of the universe have some similarities.

Such as?

The lowest entropic state is just after the BB, the highest is when all matter and energy (including heat) are distributed uniformly across the universe.

Sure. Have you ever seen heat spontaneously flow from a cold body to a hot body to which it is in thermal contact?
Of course this isn't proof as DaveC points out, but should be sufficient to convince you that the 2nd law is physically manifest.

This would only "proof" that heat doesn't flow between gases in particular. I think people here mean any process and not just gas dynamics.

Also you know the microscopic physics behind gases. So you cannot make a second law on top of it and claim both never fail. You better proof consistency between these two laws.

It's not hard, but only the people who know how to do it, can judge better what entropy means.

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How come that we have well-orderd galaxies (from randomness) with the passage of time?

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I think this question deserves more attention, because it's not at all obvious (to me) how best to answer. On the face of it, you are right: a dust cloud seems to have a high entropy, but a spiral galaxy seems to have a low entropy- how can this occur?

Calculating the entropy of a self-gravitating dust cloud may be more interesting than it first seems, I didn't find a clear reference:

Yeah the entire universe is a closed system, whereas earth is not, so entropy in our planet can increase and decrease as well. Though, when I think about it, both the lowest state of entropy and the highest state of entropy of the universe have some similarities.

The lowest entropic state is just after the BB, the highest is when all matter and energy (including heat) are distributed uniformly across the universe.

Well yes your right. However, theoretically, in case of a big crunch both the state after BB and the end of the universe would look similar. And yeah I know big freeze is a more possible end of the universe.

That is taken as a postulate, and has never been shown to be incorrect. Perhaps a cosmologist could provide a more refined answer, but from what I have read, most speculations to the contrary belong to the realm of philosophy.

The entropy of the universe as a whole is quite independent of the galaxies, nonetheless, it is mostly at the cosmic background radiation. The decrease because of the order created by the structures is negligible with respect to the total.

Although parts of the universe are in equilibrium (like a gas in a chamber), the universe in a whole is actually not, continuously expanding. So we can't actually demand it is continuously increasing in entropy, can we? It's still evolving to its equilibrium! Let's assume the big crunch is the destiny of the universe, then the universe is now already trying to reach that "equilibrium" state by slowing down. But that would imply the big bang was actually one big breach of the 2nd law. Then again, the big bang happened before time, and as soon as it happened and as soon the 2nd law came into existence, it started going to the equilibrium state of the big crunch.

Maybe I'm just talking out of my ***, it sure sounds like that reading it myself, but it is a very interesting issue worth its pondering...

Although parts of the universe are in equilibrium (like a gas in a chamber), the universe in a whole is actually not, continuously expanding. So we can't actually demand it is continuously increasing in entropy, can we? It's still evolving to its equilibrium! Let's assume the big crunch is the destiny of the universe, then the universe is now already trying to reach that "equilibrium" state by slowing down. But that would imply the big bang was actually one big breach of the 2nd law. Then again, the big bang happened before time, and as soon as it happened and as soon the 2nd law came into existence, it started going to the equilibrium state of the big crunch.

Maybe I'm just talking out of my ***, it sure sounds like that reading it myself, but it is a very interesting issue worth its pondering...

If we consider the universe to be a closed system, then in thermodynamic terms:

Touché, but I was kind of allowing fluctuations. But anyway I agree, it should decrease generally over time.

But incidentally, in the 2nd part of my post I do continue as if I presume entropy should increase so I still stand by that half of my post. Mainly: is it correct to say that if the big crunch is the end of the universe, (1) the universe is continuously increasing its entropy by slowing down for the crunch, (2) the big bang was a breach of the 2nd law (if the 2nd law can be applied to it...)

The weird thing is, aren't there some sources saying the expansion of the universe is increasing?